• Bulletin of the Korean Mathematical Society
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• v.60 no.2
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• pp.281-291
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• 2023

A normalized analytic function f is parabolic starlike if w(z) := zf' (z)/f(z) maps the unit disk into the parabolic region {w : Re w > |w - 1|}. Sharp estimates on the third Hermitian-Toeplitz determinant are obtained for parabolic starlike functions. In addition, upper bounds on the third Hankel determinants are also determined.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.165-173
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• 2018

In this paper we obtain the bounds of the third Hankel determinants for the classes $\mathcal{S}^*({\alpha})$ of starlike functions of order ${\alpha}$ and $\mathcal{K}({\alpha}$) of convex functions of order ${\alpha}$. Moreover,we derive the sharp bounds for functions in these classes which are additionally 2-fold or 3-fold symmetric.

• Honam Mathematical Journal
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• v.45 no.1
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• pp.92-108
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• 2023

We determine the upper bounds on fourth order Hankel determinants H⁽²⁾₄(f) and H⁽³⁾₄(f) for the class S^*_L of lemniscate starlike functions defined on the open unit disk which was introduced by Sokół and Stankiewicz in [17].

• Korean Journal of Mathematics
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• v.30 no.1
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• pp.81-90
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• 2022

The present investigation is concerned with the estimation of initial coefficients, Fekete-Szegö inequality, second Hankel determinants, Zalcman functionals and third Hankel determinants for certain subclasses of Sakaguchi type functions defined with subordination in the open unit disc E = {z ∈ ℂ : |z| < 1}. The results derived in this paper will pave the way for the further study in this direction.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.407-420
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• 2024

In this paper, we investigate some geometric properties of starlikeness connected with the hyperbolic cosine functions defined in the open unit disk. In particular, for the class of such starlike hyperbolic cosine functions, we determine the lower bounds of partial sums, Briot-Bouquet differential subordination associated with Bernardi integral operator, and bounds on some third Hankel determinants containing initial coefficients.

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.481-491
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• 2019

In the present paper, we investigate the upper bounds on third order Hankel determinants for certain class of close-to-convex functions in the unit disk. Furthermore, we obtain estimates of the Zalcman coefficient functional for this class.